Simplified method of evaluating integrals of powers of tangent using reduction formula as mathematical algorithm

Lito E. Suello

doi:10.1117/12.3026696

8 April 2024 Simplified method of evaluating integrals of powers of tangent using reduction formula as mathematical algorithm

Lito E. Suello

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Proceedings Volume 13090, International Conference on Computer Application and Information Security (ICCAIS 2023); 130900B (2024) https://doi.org/10.1117/12.3026696
Event: International Conference on Computer Application and Information Security (ICCAIS 2023), 2023, Wuhan, China

Abstract

One of the major topics in Integral Calculus is evaluating integrals of powers of trigonometric functions. Conventional methods use trigonometric identities to transform integrands into forms where integration formulas can be directly applied. These methods are usually long, tedious, and time consuming. Since many students are not patient enough to deal with lengthy and complicated solutions, the objective of this study is to derive direct integration formulas in evaluating integrals of powers of tangent, and to outline techniques that will simplify the solution. Expository research method was used by first deriving a reduction formula. The reduction formula was applied repeatedly to the integral of the nth power tangent until generalized equations and direct integration formulas for odd and even powers were derived. Since the derivation process involved recursive relations, the coefficients and exponents of the derived generalized equations showed certain patterns and sequences that were used as the basis in outlining simplified techniques. The derived formulas and simplified techniques can speed up problem solving since it can generate “one-liner” solutions in contrast to the long and tedious process using the conventional methods. The simplified techniques can also be used as useful inputs to computer programs (systems application process) that can generate mathematical solutions.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

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Lito E. Suello "Simplified method of evaluating integrals of powers of tangent using reduction formula as mathematical algorithm", Proc. SPIE 13090, International Conference on Computer Application and Information Security (ICCAIS 2023), 130900B (8 April 2024); https://doi.org/10.1117/12.3026696

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KEYWORDS

Algorithm development

Calculus

Mathematics

Computing systems

Differential equations

Information science

Integral transforms

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